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In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.
For instance, on September 6, 2009, the six numbers 4, 15, 23, 24, 35, and 42 were drawn from 49 in the Bulgarian national 6/49 lottery, and in the very next drawing on September 10th, the same six numbers were drawn again. Lottery mathematics can be used to analyze these extraordinary events [1].
On the other hand, if such a tiling uses exactly k of the 2 × 1 tiles, then it uses n − 2k of the 1 × 1 tiles, and so uses n − k tiles total. There are ( n − k k ) {\displaystyle {\tbinom {n-k}{k}}} ways to order these tiles, and so summing this coefficient over all possible values of k gives the identity.
An expression like 1/2x is interpreted as 1/(2x) by TI-82, [3] as well as many modern Casio calculators [36] (configurable on some like the fx-9750GIII), but as (1/2)x by TI-83 and every other TI calculator released since 1996, [37] [3] as well as by all Hewlett-Packard calculators with algebraic notation.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
For example, when =, the binomial coefficient () is equal to 6, and there are six arrangements of two copies of A and two copies of B: AABB, ABAB, ABBA, BAAB, BABA, BBAA. The same central binomial coefficient ( 2 n n ) {\displaystyle {\binom {2n}{n}}} is also the number of words of length 2 n made up of A and B within which, as one reads from ...
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
Modern computer algebra systems, as well as many scientific and graphing calculators, allow for "pretty-printing", that is, entry of equations such that fractions, surds and integrals, etc. are displayed in the way they would normally be written. Such calculators are generally similar in appearance to those using infix notation, but feature a ...